I do believe that one shots and small games don’t need any kind of xp. But if there is any mechanic character advancement, maybe others things can be used?
I don’t use xp, but I do that x adventures can level you up. But if someone just joined the party, he may not have accomplished x adventures. So, even if not giving xp, there still an bargain chip.
I don’t have a problem with xp, and I preferred to give by treasure and by adventure, so killing was not the objective
I like your philosophy but I have a different conclusion from it. I think most ttrpg players are at least subconsciously aware that xp is not the real reward the player is looking for from the game. But, unless the game is specifically about not changing, we expect some sort of game structure to modify the characters we play. Since a grand majority of games are about a narrative of getting stronger, we would expect the reward for the character to be points/dots/chits/etc that allow them to grow. You can give rewards based on mechanical or narrative achievement, but I think if we plan to spend 4+ hours (minimum) with these characters, we want them to evolve if only to not get bored.
But, unless the game is specifically about not changing, we expect some sort of game structure to modify the characters we play
Isn’t this a weird answer on a question that asks “Is XP a vestigial design element in some modern games?” 
And there is more to “change” than just numeric advancements (that rarely do something because the game master will normally raise the stakes anyways).
Not only numbers change, but some sort of reward, like a new ability.
I do believe there’s a way, like your improvement can apply by gears
Character change certainly isn’t limited to abilities becoming more powerful, but I don’t think it’s a stretch to say that we can leverage “xp” (by which I mean, any sort of mechanical reward) to change (change, not specifically improve) the characters. I’m approaching this with the attitude that the mechanical parts of a ttrpg should be interacting with the characters, in a response to both their mechanical and emotional actions. From my point of view, if the RP isn’t interacting with the G, then you don’t strictly have an RPG, but a game in which roleplaying also happens
(For the record, there’s nothing wrong with that, games are great, no matter how they do or don’t conform to type/genre. But I’m writing my opinion based on my understanding of RPGs and responding in how I interpret this conversation in relation to them)
I think “XP incentivizes players to do things” is one of those useful design tips that can get hardened into a dogma. Incentivizing certain actions is not the only thing that XP does. For example, I’ve been thinking about the stat highlighting mechanic in Apocalypse World. You could analyze that in incentive terms – I’m paying you in XP to roll Seduce or Manipulate Someone more often. But you could also look at it as a sort of communication about the direction of the story – let’s see your character develop in a way that puts more emphasis on their social interactions. In the latter framing, highlighting Hot both communicates a desire for a certain story direction, and engages a mechanic to support it.
Ultimately, XP is a currency, and most games are built around earning and spending the game’s various currencies. So in that sense, XP is no more vestigial than strings or +1 forwards.
That seems needlessly utilitarian. There are lots of parts or RPGs that are not “important”, but also useful to have as part of the game. Monsters having different move speeds or sizes is not what DnD is “about”, but the sum of many related things builds the theme and atmosphere. I feel like either I am not communicating clearly or you are focusing on only some of my arguments at the expense of others. I have been consistently saying that the mechanical “rewards” from a system do not need to strictly be upgrades/improvements, only that in my mind it feels important for the the mechanical system of the game to be interacting with the fiction/roleplay of the game as oppose to them being two distinct things that happen when we play a ttrpg
I did, and while I’m not trying to make any authoritative or absolute statements (I certainly hope you are assuming everything I state in this forum is “my opinion” without me having to reiterate), I am stating, from my point of view, for most ttrpgs (75%+), no, “xp”, at least in the way I understand it, is not vestigial. Yes, for some games (like every one-shot), xp doesn’t matter, but if we’re going to approach this discussion from that general an approach, why even bother having it? If we took that position then the answer to every hypothetical would be “yes”
I apologize if this post comes off as a rant, but in my short time here I have been trying to articulatey honest opinion (stressing opinion) and response to discussions that interest me. If I need to improve my tone, ok, please let me know how I am improperly stating my arguments, but I would also appreciate that my statements be taken as a legitimate viewpoint to be responded to and discussed without me needing to preface every post with “I do not presume to be objectively correct, but IMO”